I bought a new laptop and don't know how to connect my 003Rack (firewire) via the TypeC USB port. Does anyone know if there is a adapter solution or something?
Many thanks.

Nope because we don't know what computer you actually have and what type of USB-C port it has. USB-C can optionally provide USB (and several different versions of that), Thundertbolt and DisplayPort protocols.

USB-C connectors do not provide Firewire, which you need to drive the 003.

If its a MacBook Pro with USB-C with Thunderbolt 3 then Apple makes a a USB-C Thunderbolt 3 to Thunderbolt 2 adapter, and a Thunderbolt 2 to Firewire 800 adapter, then you use a Firewire 800 to 400 adapter or cable. You chain that lot together and it will do what you need.

Most USB-C connector on PCs don't provide Thunderbolt and you can't adapt from them to Firewire.

The USB Type-C ports on your laptop only support USB 3.1 Gen 1 (which is to say they are USB 3.0 5Gbps) and not Thunderbolt 3, so no use to you.

Yes you posted on the Windows Forum, I mentioned Macs so you can be clear about the difference, and for example know that you cannot use those Apple adapters on your laptop.

There is no way to connect your laptop to your 003 firewire interface.

You need a different laptop or a different (USB or Ethernet (e.g. Dante)) interface. If you are running old Pro Tools LE that is licensed off the 003 you will also need to upgrade from Pro Tools LE to Pro Tools if using a non-Avid interface.